Certain applications for bandpass filters require variation of filter bandwidth without attendant variation in gain. FIG. 1 shows a signal source 11 connected to a prior art bandpass filter 39 and to a reference voltage source 10. Signal source 11 generates a signal S.sub.in which has a signal voltage V.sub.i. Bandpass filter 39 includes a crystal resonator 32 and a variable resistance 33. A signal S.sub.out having a voltage V.sub.o appears on an output node 16.
As shown in FIG. 2, crystal resonator 32 may be modelled (neglecting shunt capacitance) as an inductor 45, a capacitance 46 and a resistance 47 (the magnitude of resistance 47 is referred to in the formulae herein as R.sub.47) connected together in series.
Varying resistance 33 varies the bandwidth of bandpass filter 39, but also varies the passband gain (V.sub.o /V.sub.i) of filter 39 because of voltage division between resistance 47 and resistance 33. A first prior art method which allows the variance of resistance 33 without varying the passband gain requires generating a signal source with a negative source resistance. The negative source resistance has a magnitude in ohms of negative R.sub.47, thus cancelling resistance 47. A second prior art method requires amplifying the signal before or after filter 39, the amount of amplification being a function of the value of resistance 33.
Both the aforementioned prior art methods have drawbacks. The first method requires negative source resistance, thus requiring positive feedback. Positive feedback may multiply noise and distortion thus degrading the performance of bandpass filter 39. The second method requires a variable gain amplifier which must be able to automatically adjust its gain as the magnitude of resistance 33 varies.